A coffee business orders paper cups by the carton, with each carton costing $10. The company uses an average of 50 cartons per week (assume that there are 52 weeks per year, for simplicity), with a standard deviation of 12 per week. The fixed cost to place an order, independent of the order quantity, is $40 per order; the annual holding cost for inventory is estimated to be 20% of inventory value. If the company seeks to order in lot sizes (order quantities) that minimize the total annual holding plus ordering costs, how many should they order at a time?

a.

1 to 100 units

b.

101 to 200 units

c.

201 to 300 units

d.

301 to 400 units

e.

more than 400 units